If x approaches a certain number as one goes to infinity and negative infinity, then there is a horizontal asymptote. If it only approaches infinty or negative infinity as it approaches positive/negative infinity, then there is no horizontal asymptote.
Ex: lim f(x)=7
x-->+/- infinity (There would be a horizontal asymptote at y=7)
There exists at horizontal asymptote at y=0 if the function given has some constant over x to a certain exponent.
Ex: lim 7/(x^3)= 0 or if the function was 6 - (function used before), then there would be an asymptote at 6
infinity
Ex: lim f(x)=7
x-->+/- infinity (There would be a horizontal asymptote at y=7)
There exists at horizontal asymptote at y=0 if the function given has some constant over x to a certain exponent.
Ex: lim 7/(x^3)= 0 or if the function was 6 - (function used before), then there would be an asymptote at 6
infinity